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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

0 votes
1 answer
161 views

Sufficient and necessary condition for the global uniqueness of fix-points

https://www.ams.org/journals/proc/1976-060-01/S0002-9939-1976-0423137-6/S0002-9939-1976-0423137-6.pdf This paper gives a sufficient condition for the uniqueness of SCHAUDER fix point. I wonder if the …
High GPA's user avatar
  • 263
1 vote
0 answers
385 views

The perturbation of a convex function can also be convex?

$ W^{1,\infty}(D)\ni f:D\to\mathbb R, (x,y)\mapsto f(x,y)$, is a strictly increasing on both dimensions (i.e. if $x_1>x_2$ then $f(x_1,y)>f(x_2,y)$), lipschitz continuous function defined on a convex …
High GPA's user avatar
  • 263
5 votes
1 answer
305 views

Reference for the rectifiablity of the boundary hypersurface of convex open set

The boundary of any convex open set $X$ is $\mathbb R^n$ is a rectifiable hypersurface. To see this, intuitively, simply take a sphere $S_d$ with diameter $d\in(0,+\infty]$ that contains $X$. The …
High GPA's user avatar
  • 263